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GATE 2020: Toppers Weekly Quiz 1 (App update required to attempt this test)

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Question 1

Read each sentence to find out whether there is any grammatical mistake/error in it. The error if any will be in one part of the sentence. Mark the number of that part with error as your answer. If there is ‘No error’, mark (5).
The Board's decision has provided (1)/ employees with the opportunity (2)/ to acquire up to 100 (3)/ shares by the company. (4)/ No error (5)

Question 2

In the sentence given below, two words are missing. Identify the correct option from the given options to complete the sentence:
____ by its inability legally to confiscate a contraband shipment from an insurgent country that was intercepted by the Coast Guards earlier this year, the government decided to set up a new _______ to crackdown on such trade.

Question 3

Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one-way ticket fare of the trip for single person is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs____.

Question 4

Let A be a 3x3 singular matrix with two of its eigen values as 2 and 3. The number of linearly independent vectors of

Question 5

The roots of ax² + bx + c = 0 are real and positive, a, b and c are real. Then ax² + b| x | + c = 0 has

Question 6

Chernobyl – 1^st nuclear disaster left world in shock; reason was human error. Scientist suggested that there was no way in which a reactor core can explode but mathematically it was possible.

Hypothetical situation: There were 4 reactors in Chernobyl nuclear power plant

Reactor A: 1000 Cooling rods

Reactor B: 2000 Cooling rods

Reactor C: 3000 Cooling rods

Reactor D: 4000 Cooling rods

Probability of failure of any cooling rod is = 0.001

If reactor explodes, probability of Explosion in Complete power plant is half to that of probability of explosion of reactor. If probability of explosion for all reactors is same & power plant exploded, what is the probability it is due to explosion in reactor B?

Question 7

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straightlines to its corners, how many (new) internal planes are created with these lines?

Question 8

There are 5 tickets with number 1 to 5, out of which 3 ticket are chosen in order. Probability that number on ticket will follow arithmetic progression varies in two parts:

a) Number in order will only be accepted – P {ordered pair)

b) Number in random order will also be accepted – P {random)

Find the probability P {ordered pair)/ P {random)

Question 9

Find the DFT of y[m] if y be the discrete signal, periodic of order m, y = (1,

Question 10

Question 11

If 137 + 276 = 435 how much is 731 + 672?

Question 12

Solve the equation y = 2Px + Pⁿ, find the value of y in term of P.

Question 13

Find by double integration the volume of the solid generated by revolving the ellipse

about the x-axis.

Question 14

Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

Question 15

A water tank of capacity 6000 litres is connected to 2 taps ’A’ and 'B'. Water flows from these 2 taps at 90 litres per minute and 60 litres per minute respectively. To fill this empty tank, first tap ‘A’ is opened for sometime and once it is closed, tap ‘B’ is opened till the tank is full taking a total of 90 minutes.What is the difference in the time (in minute) for which the taps are opened to fill the tank.

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ESE & GATE EE Engineering Mathematics General Aptitude

Dec 29ESE & GATE EE